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2 years ago

If Betty makes monthly deposits at the end of each month in an account that earns 8% interest compounded monthly,

Mathematics

1 answer:

Svetlanka [38]2 years ago

4 0

9514 1404 393

Answer:

(a) $254.08

(b) $767.34

Step-by-step explanation:

These questions are best answered by a financial calculator or app. Such are available for your phone or tablet. A spreadsheet also has built-in functions for making these calculations.

(a) FV = $40,000, i = 8% per year, n = 9 years (108 months), compounding 12 times per year. The monthly deposit needs to be $254.08.

(b) Payment = $254.08, n = 3 months, i = 8%/year, compounding 12 times per year. FV = $767.34.

108 × $254.08 = $27,440.64

The interest earned is enough to bring the account value to $40,000, so is ...

$40,000 -27,440.64 = $12,559.36

_____

<em>Additional comment</em>

The amount $254.08 is rounded down to the nearest cent, so the balance after 9 years will be $39,999.70, which is $0.30 short of $40,000. We used $40,000 as the final account balance, so overestimated the interest by $0.30.

There may be additional small changes in the values if you round interest to the nearest cent each month the way a financial institution would. It is hard to tell in these problems how accurate you're intended to be in your calculations.

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